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**ENGINEERING MATHEMATICS-I****[As per Choice
Based Credit System (CBCS) scheme]****(Effective from
the academic year 2015 -2016)****SEMESTER - I/II**

Subject
Code - 15MAT11

IA Marks -
20

Number of
Lecture Hours/Week - 04

Exam Marks
- 80

Total
Number of Lecture Hours - 50

Exam Hours
- 03

CREDITS -
04

**Course Objectives:**

To enable
the students to apply the knowledge of Mathematics in various engineering
fields by making them to learn the following:

•nth
derivatives of product of two functions and polar curves.

•Partial
derivatives

•Vector
calculus

•Reduction
formulae of integration; To solve First order differential equations.

•Solution
of system of linear equations , quadratic forms.

**Module - 1**

**Differential Calculus -1**: determination of nth order derivatives of

Standard
functions - Problems. Leibnitz’s theorem (without proof) - problems.

**Polar Curves**- angle between the radius vector and tangent, angle between two curves, Pedal equation of polar curves. Derivative of arc length - Cartesian, Parametric and Polar forms (without proof) - problems. Curvature and Radius of Curvature – Cartesian, Parametric, Polar and Pedal forms

(without
proof) -problems

**Module -2**

**Differential Calculus -2**

Taylor’s
and Maclaurin’s theorems for function of one variable(statement only)-
problems. Evaluation of Indeterminate
forms.

**Partial derivatives**– Definition and simple problems, Euler’s theorem(without proof) – problems, total derivatives, partial differentiation of composite functions-problems. Definition and evaluation of Jacobians

**Module – 3**

**Vector Calculus:**

Derivative
of vector valued functions,
Velocity, Acceleration and related problems, Scalar and Vector point
functions. Definition of Gradient, Divergence and Curl-problems. Solenoidal and

Irrotational
vector fields. Vector identities - div(ɸA), curl (ɸA ), curl(
grad ɸ), div(curl A).

**Module-4**

**Integral Calculus:**

Reduction
formulae - (m and n are positive
integers), evaluation of these integrals with standard limits (0 to π/2) and
problems.

**Differential Equations ;**

**Solution of first order and first degree differential equations**– Exact, reducible to exact and Bernoulli’s differential equations .Orthogonal trajectories in Cartesian and polar form. Simple problems on Newton's law of cooling.

**Module-5**

**Linear Algebra**

Rank of a matrix by elementary
transformations, solution of system of linear equations - Gauss-elimination
method, Gauss –Jordan method and
Gauss-Seidel method

Eigen
values and Eigen vectors, Rayleigh’s power method to find the largest Eigen
value and the corresponding Eigen vector. Linear transformation,
diagonalisation of a square matrix .

Reduction
of Quadratic form to Canonical form

**Course outcomes:**

On
completion of this course, students are able to

•Use
partial derivatives to calculate rates of change of multivariate functions.

•Analyze
position, velocity, and acceleration in two or three dimensions using the
calculus of vector valued functions.

•Recognize
and solve first-order ordinary differential equations, Newton’s law of cooling

•Use
matrices techniques for solving systems of linear equations in the different
areas of Linear Algebra.

Question
paper pattern:

•The
question paper will have ten questions.

•Each full
Question consisting of 16 marks

•There will
be 2 full questions(with a maximum of
four sub questions) from each module.

•Each full
question will have sub questions covering all the topics under a module.

•The
students will have to answer 5 full questions, selecting one full question from
each module.

**Text Books:**

1. B.S.
Grewal, "Higher Engineering Mathematics", Khanna publishers, 42nd
edition, 2013.

2. Erwin
Kreyszig, "Advanced Engineering MathematicsI, Wiley, 2013

Reference
Books:

1. B.V. Ramana, "Higher Engineering M
athematics", Tata Mc Graw-Hill, 2006

2. N.P.Bali and Manish Goyal, "A text
book of Engineering mathematics”, Laxmi publications, latest edition.

3. H.K. Dass and Er. RajnishVerma,
"Higher Engineerig Mathematics", S.Chand publishing, 1st edition,
2011.

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